New Framework for Sequences With Perfect Autocorrelation and Optimal Crosscorrelation
Minkyu Song, Hong‐Yeop Song · IEEE Transactions on Information Theory · 2021
In this paper, we give a new framework for constructing perfect sequences, called generalized Milewski sequences, over various alphabets including Polyphase (PSK) as well as Amplitude-and-Polyphase (APSK) in general, and for constructing optimal sets of such perfect sequences by using combinatorial designs, called circular Florentine arrays. Specifically, we prove that, given any positive integer$m\geq 1$, (i) there exists a perfect sequence of period$mN^{2}$for any positive integer$N$if there exists a perfect sequence (polyphase or not) of length$m$; (ii) an optimal$k$-set of perfect sequences of length$mN^{2}$can be constructed if there exist both a$k \times N$circular Florentine array and an optimal$k$-set of perfect sequences all of length$m$. This enables us to find some optimal$k$-set of perfect sequences where$k > p_{\text {min}}-1$, where$p_{\text {min}}$is the smallest prime factor of$mN^{2}$.